Multi-state unclonable functions and related systems

ABSTRACT

The present disclosure relates to implementations of physically unclonable functions (PUFs) for cryptographic and authentication purposes. Specifically, the disclosure describes implementations of machine learning engines (MLEs) in conjunction with PUFs generating outputs having multiple states.

FIELD OF THE INVENTION

The present disclosure relates to implementations of physicallyunclonable functions (PUFs) for cryptographic and authenticationpurposes. Specifically, the disclosure describes implementations ofmachine learning engines (MLEs) in conjunction with PUFs generatingoutputs having multiple states.

BACKGROUND OF THE INVENTION

A PUF is a physical device or function whose output depends upon thedevice's physical characteristics. The physical characteristics, such ascritical dimensions, doping levels of semiconducting layers, andthreshold voltages, make the devices unique and difficult to duplicate.PUF may therefore be utilized as a hardware implementation of a one-wayfunction.

PUFs are strengthening the level of security of emerging data securitymethods. In such systems, PUFs operate as a set of cryptographicprimitives useful in authentication procedures. The underlying mechanismof PUF authentication is the creation of a large number of challenge(i.e. Input) response (i.e. output) pairs (called CRPs) that are uniqueto each PUF device. Once deployed during an authentication cycles, thePUFs are queried with challenges. Authentication is granted when therate of matching responses is statistically high enough.

In various authentications, the challenges are stored in a secure servercoupled to the device being prepared for authentication. Once generatedduring the authentication cycles, the challenges are then used inchallenge queries. Authentication is granted by the system when the rateof matching responses between the PUF-generated CRPs is sufficientlyhigh enough above a threshold value. Weak PUFs generally only produce asatisfactory rate of responses far from 100% matching, while with strongPUFs the rate approaches 100%.

Over time, however, PUFs are subjected to a set of physical parameters,such as temperature, aging factors, bias voltage drifts, andelectrostatic interferences that cause the output of a PUF to changeover time. In conventional implementations, this varying output canresult in an increased and undesirable error rate. A number of differenterror correction coding (ECC) techniques have been developed in anattempt to reduce intra-PUF output variations. These approaches,however, generally cannot overcome the relatively high data error ratein subsequent read-outs of PUF in the presence of environmentalvariations.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated by way of examples, embodimentsand the like and is not limited by the accompanying figures, in whichlike reference numbers indicate similar elements. Elements in thefigures are illustrated for simplicity and clarity and have notnecessarily been drawn to scale. The figures along with the detaileddescription are incorporated and form part of the specification andserve to further illustrate examples, embodiments and the like, andexplain various principles and advantages, in accordance with thepresent disclosure, where:

FIG. 1 is a diagram illustrating the generation of multi-state outputsfrom a PUF device.

FIG. 2 is a block diagram illustrating a method for challenge generationusing a PUF device.

FIG. 3 is a table illustrating an error rate and vector of errors for aRCP for a PUF device in which the CRP error rates, Ei, may be derivedfrom analysis of experiments performed on ReRAM devices.

FIG. 4 is a block diagram illustrating a method for authentication inaccordance with the present disclosure.

FIG. 5 is an illustrating an approach for implementing CRP evaluationusing an MLE.

FIG. 6 is a block diagram illustrating an error correctionimplementation incorporating an MLE in accordance with the presentdisclosure.

FIG. 7 is a diagram illustrating a Gray encoding scheme.

FIGS. 8A-8B are block diagrams illustrating techniques for errorcorrection in accordance with the present disclosure.

FIG. 9 is a block diagram illustrating implementations of authenticationsystems that utilize PUFs in combination with a crypto-machine learningengine.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present disclosure relates to implementations of physicallyunclonable functions (PUFs) for cryptographic and authenticationpurposes. Specifically, the disclosure describes the implementations ofmachine learning engines (MLEs) in conjunction with multi-state PUFs.

In the present system and method, the outputs of a particular PUF deviceare sorted into a plurality of different states arranged to capture aprofile of the physical parameters determining the operation of the PUF.Because the multiple states are tied to the PUF's physicalcharacteristics, the multi-state output of the PUF enables a predictionof error rates for the PUF's output. For a particular PUF device theseerror rates stay constant, even when the PUF device is subjected tonatural effects such as aging, temperature changes, bias voltagesdrifts, and electrostatic interferences. As such, a Machine LearningEngine (MLE) can analyze the current output of the PUF device inconjunction with the PUF's known and predictable error rates to accountfor variations in PUF output over time. Natural drifts of the PUF'soutput therefore do not result in errors such as negativeauthentication, while statistically abnormal challenges may still becaught and flagged as a strong negative authentication.

FIG. 9 illustrates one implementation of an authentication system thatutilizes PUFs. A server initially queries the system with a challenge.After receiving the initial challenge, a response is generated by thePUF 200. This response, as well as a mapping of the multi-states andsensing of the parameters surrounding the PUF 200 (e.g., temperature,age, and the like) are returned to a crypto MLE 900. The Crypto-MLE 900process the response received from the PUF 200 as well as themulti-state data and sensing information using PUF models 910, and alearning data base to produce an output to the server. The outputgenerated by the Crypto-MLE 900 indicates a positive or negativeauthentication.

In the present system and method, a machine learning engine 220 (MLE) isconfigured to analyze the output of a multi-state PUF 200 based on achallenge or response generation process that captures unique attributesof the physical elements underling the PUFs in a multi-state memory 210.The MLE 220 then implements an authentication process that quantifiesthe profile of the PUF's CRP error rates in addition to the surroundinginput and environmental parameters (such as ambient temperature and ageof the PUF 200). A computation is then performed by the MLE 220 tofinalize the authentication process. In the present disclosure variousexamples are presented in which PUF challenge and responses have a sizeN of 128 bits. But it will be understood that the present system andmethod may be utilized in accordance with PUFs having differentchallenge and response sizes and different configurations.

A PUF 200 may be implemented as an array of memory cells. Each cell inthe memory array may be implemented, for example, as a resistive randomaccess memory (ReRAM) element, whose conductivity is determined by avoltage supplied to the memory cell, though other configurations may beused as well. Using such a memory array, a challenge may be created bysweeping the voltage supplied to each memory cell in the array todetermine at what input voltage the cell's conductivity changes and thecell switches from storing a logical value of “0” to a logical value of“1”. This voltage is referred to as Vset for that memory cell. Due tothe physical attributes of the memory array, different cells will switchlogical values at slighting different Vset voltages. Those varying Vsetvoltages can be used to create a challenge for a particular PUF 200device. For example, a challenge may be created by allocating aparticular cell in the array a value of “0” if the Vset voltage at whichit changes state falls below a threshold value. Conversely, a particularcell may be allocated a value of “1” if the Vset voltage at which itchanges state is equal to or greater than the threshold value. Thechallenge is then a stream of bits whose values are determined by theVset values allocated to each cell in the memory array.

Once extracted from the memory array, the challenge may be sent to andstored within a secure server 230. Concurrently, as shown FIG. 1, thevarious cells in the memory are sorted into different groups based uponthe Vset value at which the cells switched from a logical value of “0”to a logical value of “1”. Because that particular Vset value is atleast partially determined by the physical parameters of the cells, thisinvolves grouping the cells based upon the physical parametersunderlining each cell of the memory.

In the example depicted in FIG. 1, the 16 memory cells of the total 128cells with the lowest Vset values are allocated to a group with state 0,the following 16 cells with higher Vset values are allocated state 1,all the way to the 16 cells with the highest Vset value that areallocated state 7. In this manner, the cells of the memory are sorted in8 different states.

Because the Vset value for a particular cell is determined at leastpartially by the physical attributes of the cell, the cells that areeach grouped together within the same group will tend to share somephysical attributes. The groupings, therefore, provide useful knowledgeabout the cells themselves and, as described in detail below, providessome information regarding the likelihood of the various cells to changestate given a particular set of environmental conditions.

The precise mapping of the PUF 200 memory array (e.g., the PUF'schallenge bit stream as well as the groupings of cells within the PUF200) can be stored in a secure memory during the challenge generationprocess, this configuration is referred to below as Option A. Analternative method of equivalent efficiency is to extract the mappingduring the response generation process, this configuration is referredas Option B.

To reiterate more generally, a PUF 200 of N bits is sorted into nstates, either during challenge generation, or response generation. Eachstate i is allocated to ni cells in such a way that Σ_(ni=1) ^(ni=n)ni=N. The overall block diagram showing how the challenge generationprocess is done is shown FIG. 2 through an MLE 220 that manages theentire secure PUF system.

With an initial challenge generated for the PUF 200 and stored in securememory, the PUF 200 may be utilized to generate responses as part of aCRP. As described above, over time the output of the PUF 200 may varydue to environmental factors, resulting in an error or variance in theoutput of the PUF 200.

The PUF 200 responses may be generated in the same manner as thechallenges, described above. The responses are typically created inresponse to a new request for authentication or the initiation of acryptographic function. As shown FIG. 3, differences or errors in theCRPs are expected considering that the physical parameters of the PUFsare naturally evolving over time and so the output of the PUF 200changes over time. For example, temperature changes over time mayincrease the likelihood of CRP errors.

For a given cell k that is part of the PUF 200, the CRP error betweenthe challenge Ck and the response Rk is given by the equation:ΔCRPk=|Rk−Ck|

Where ΔCRPk is the CRP error rate of the cell k. For the populations ofni cells that are part of the state i the average CRP error rate isgiven by:

${Ei} = {\frac{1}{n_{i}}{\sum\limits_{k = 1}^{k = n_{i}}{{{Rk} - {Ck}}}}}$

The average error rate for the n states is given by a Vector of Error VEthat is characteristic of a particular response:VE=E ₀ ,E ₁ , . . . ,E _(i) , . . . ,E _(n)

This description of CRP error rates, and the resulting Vector of erroris applicable to both Option A and Option B described above. In the caseof Option A, the grouping of memory cells by state is done during thechallenge generation process while it is also done during the responsegeneration process for Option B. As shown below these Vectors of Errorsare used to complete the authentication process.

When utilizing the present multi-state PUF 200 implementation, themajority of errors (that is, difference between the bits of thechallenge and response values) are likely to occur for memory cellssorted into the groups around the threshold Vset value. With referenceto table 3 of FIG. 3, for example, groups 3 and 4 (shown in FIG. 1 to bethe groups directly on either side of the threshold Vset voltage)exhibit a significantly higher likelihood for errors that cellsbelonging in the other groups. This results because those cells may onlyrequire small changes in environmental conditions to change the Vsetvalue at which they change state. The other cells (e.g., those cellsthat are members of groups 0, 1, 2, 5, 6, and 7) would require moresignificant variances in environmental conditions to change theirbehavior and so are less likely to result in changes and, therefore,errors.

The vector of error described above, therefore, may be supplied to anMLE 220 which can use the vector of error to identify which values in aCRP have been generated by reliable memory cells (e.g., those cellsbelonging to groups 0, 1, 2, 5, 6, and 7) and which values weregenerated by unreliable memory cells (e.g., those cells belonging togroups 3 and 4). Differences in the CRP occurring in unreliable memorycells may therefore be given less weight and made less likely to resultin a mismatch or error condition than more reliable cells.

FIG. 4 illustrates an authentication scheme implemented by an MLE 220 inconjunction with the present multi-state PUF 200. In step 1, a secureserver 230 sends a challenge to the MLE 220. The MLE 220 requests thatthe PUF 200 generate a fresh response in step 2. In step 3, the MLE 220gathers the response from the PUF 200, as well as all available data tocompute a secure authentication.

Then, in the case of Option A, in step 4 the MLE 220 retrieves themapping of the multi-states of the PUF 200 from the secure memory, whilein the case of option B in optional step 4 a fresh mapping of themulti-states is generated during the response generation process. TheMLE 220 handles the communication between the secure server 230 and thePUF 200, and can be integrated in a secure element containing acrypto-processor, the secure memory, and the PUF 200.

The MLE 220 can then evaluate the response received from the PUF 200 todetermine whether any differences between the response and the challengereceived in step 1 may be attribute to natural drifts in the PUF'soperation over time (e.g., that are attributable to environmentalchanges) or whether the differences are attribute to suspicious causes(e.g., a malformed or false challenge). In performing the evaluation,the MLE 220 may rely upon the vector of error, described above,environmental conditions of the PUF 200, historical values for prior PUFresponses, and other information describing how the PUF responses mayvary according to different ambient conditions. FIG. 5, for example,illustrates the data inputs supplied to the MLE 220 in performing thepresent authentication analysis. In one implementation, the MLE 220 maybe configured to examine the CRP using the following information:

-   -   A Vector of Error: VE_(j)=(E₀, E₁, . . . , E_(i), . . . ,        E_(n))_(j) for the PUF 200.    -   A Vector of Input: I_(j)=(I₀, I₁, . . . , I_(l), . . . ,        I_(m))_(j) that describes all parameters that could be available        to the MLE 220 describing the current operating conditions of        the PUF 200 including operating temperature, biasing voltage and        current conditions, as well as the level of electro-magnetic        noise.    -   A Learning data base that incorporates a record of prior        responses from the PUF 200.    -   Generic predictive models describing the laws of physics        underlining the physical parameters of the PUF 200. For example        the impact of temperature on the physical parameter is usually        well described by predictive models.

In step 5, having evaluated the CRP in view of the available vector oferror and environmental data, the MLE 220 determines whether the CRP isvalid and issues a response to the secure server 230 accordingly.

A design criteria for implementing the algorithms by which the presentMLE 220 evaluates CRPs for a particular PUF 200 includes achievingrelatively high inter-PUF device and low intra-PUF device Hammingdistances. The inter-device distance is measured as the average Hammingdistance between the responses of two PUF devices to the same challengethat shows the uniqueness of PUF responses. However, the intra-devicedistance measures the average Hamming distance between the responsesfrom a PUF 200 to the same challenge applied at different times andenvironmental situations. A larger Hamming distance results in lowerprobability that a noisy readout of a particular PUF 200 will be mappedto another identity in database (lower false acceptance rate). Onemethod to reduce the false acceptance rate and false rejection rate isincreasing the length of output bits in the CRP.

The changes in environmental conditions and also an aging factor canresult in minor mismatches in circuit components, hence the PUFresponses to the same challenge can be affected by noise. Thesepotential variations may occur due to random noise at terminal signalssuch as source, drain and gate or changes in temperature or voltage oraging effects (deterministic noise). The natural and physical causesbehind the deterministic portions of noise suggests the possibility oflearning this behavior over the course of different response generationsby a PUF 200 and the use of this as a-priori information in errordetection and correction for later response generations. Use ofadditional error correction modules may also combat the effects ofrandom noise within the present authentication system.

In one embodiment, error correction codes and machine learningalgorithms are combined to combat both random and predictable potentialnoise sources in a PUF 200. FIG. 6 is a block diagram illustrating howthis approach may be based on a multi-level iterative decoding method toimprove the performance of error correction through utilization ofintrinsic reliability information in data. The approach also utilizesiterative decoding between two decoder modules (see FIG. 8B) in whichthe soft output of each decoder is fed as a-priori information to theother module to improve its decoding accuracy till converging to adesired performance. This design may considerably reduce the errorprobability.

Since a portion of PUF 200 error may be due to physical andenvironmental factors, these types of errors can be learned andpredicted using information available from experiments on differentPUFs. This form of error prediction—based upon historical rates of errorin real-world PUF devices—may be utilized to correct errors resultingeven after ECC has been implemented. Since these errors could have beencaused due to several factors such as the variations in temperature,voltage and current, an Independent Component Analysis (ICA) technique(see FIG. 6) may be used to break down this error to a summation ofknown possible causes. Independent component analysis involves thedecomposition of a random vector in linear components that arenon-Gaussian and independent or as independent as possible. Whenimplementing ICA, the assumption of independency among the variables canbe relaxed to address the possibility of correlation among the physicaland environmental factors that may cause variations in PUF 200 readoutsor outputs. Then each of the error terms may be corrected using machinelearning algorithms knowing the available data sets that are associatedwith variations due to each of these parameters.

In some instances, when performing error correction, the multi-state CRPgeneration method described above and illustrated in FIG. 1 may beutilized within a multi-level soft decision correction method based oniterative decoding. In such an approach, the PUF 200 readouts are firstquantized to 8 different levels (though in other embodiments differentquantizations of PUF 200 readouts may be utilized) that enable ameasurement of readout reliability. Quantizing the PUF 200 readouts intodiscrete groups enables, as discussed above, a measurement of errorprobability. A Euclidean distance between CRPs is generated by comparingthe response from the PUF 200 to a given reference vector from thechallenge. This model, in which PUF 200 readouts are assigned todifferent groups, is therefore able to further distinguish the accuracyand reliability of the readouts from the PUF 200 in comparison to abinary model since the model provides more information regarding thedistance of the readouts from the Vset threshold.

When processing the challenge, the states associated with each readoutvalue from the PUF 200 can be mapped to a binary notation using a Graycoding method. FIG. 7 is an illustration comparing a Gray encodingmethod to a conventional binary encoding method for decimal valuesranging from 0 to 7. Each bit of the challenge string may be encodedusing two independent Binary Bose-Chaudhuri-Hochquenghen (BCH) codingmodules based on code-offset techniques and corresponding redundant orhelping data that has been added to the input signal. The challengestring is then encrypted using a hash function and made available aspublic information. When processing the responses, the PUF 200 readoutsin the response to the challenge are passed through a similar process ofquantization and Gray coding and the extracted information is combinedwith the publicly available helping data. The difference between thecode-words extracted from the challenge and response is transformed tosoft information and is fed to the iterative parallel concatenationdecoding structure.

The present coding structure is based on multi-state input and aniterative parallel concatenated decoding using soft decision decoding.In hard decision decoding, the output is made up of a set of specificvalues (in the case of binary values, 0 and 1), however in soft decisiondecoding the output instead presents the reliability of each bit, e.g.how close the reading is to the thresholds for 0 or 1, instead of savingthe results in binary as a hard decision. Therefore, the present methodcan improve PUF 200 data estimation accuracy by using the intrinsicreliability information in a concatenated structure. Furthermore, thismethod can eliminate the need for having a large initial data string toobtain a required accuracy.

In the present embodiment, each readout (Ri) from the PUF 200 isquantized to a state value from the finite set of (s1, s2, s3, . . . ,sQ), where Q=^(2M), where Q and M denote the number of non-overlappingstates and the number of bits, respectively. The quantization can beperformed using common uniform midrise quantization methods, forexample. Since the PUF 200 readouts may follow a Gaussian distribution,it could be possible to use a Lloyd-Max quantizer as an optimum designfor Gaussian distributed input.

In one embodiment, Gray coding is used to map the state information tobinary data to be transmitted between the server and PUF 200. In a Graycoding scheme, adjacent states only differ in one bit. The Gray codingimplementation for the case of 8 states is depicted in FIG. 7. The useof the Gray coding scheme can result in enhanced error resiliency of theproposed method.

In some embodiments, the present system may utilize turbo-inspiredforward error correction codes. Turbo codes describe a class ofhigh-performance ECCs utilized in various forms of electroniccommunications. Two features of turbo codes are i) the use of apseudorandom interleaver 800 between the two coding components, and ii)an iterative decoding structure with a soft-input soft-output (SISO)decoder. The interleaver 800 distributes potential error in a datawordover different datawords and consequently increases the probability oferror correction. In an iterative decoding design, the soft input of onedecoder is fed to the other decoder and vice versa, until the finaldecoding results converge with a desired accuracy. The turbo codes aremost commonly built up as a parallel concatenation of two RecursiveSystematic Convolutional (RSC) codes. However, these will have anefficient performance for a long data string that may not be the case insome PUF 200 applications. Also for long input lengths, thecomputational complexity of the decoding process may become intractable.

Accordingly, an embodiment of this disclosure may use linear block codeswith a turbo-inspired parallel concatenated coding structure anditerative decoding nature to obtain the benefits of accurate errorcorrection with an acceptable data string length. Different codingcomponents such as BCH and Reed Solomon (RS) can optionally be utilizedin this model.

Coding can be performed through a multi-stage parallel coding structure.For simplicity, FIG. 8A illustrates a turbo-inspired parallelconcatenated encoding scheme in which a random interleaver 800 isdisposed between encoding modules.

The random interleaver 800 is utilized between the two parallel codingcomponents to distribute the possible error over the codeword andproduce a random-like property. This enables the shuffling of PUF 200outputs while keeping the linear behavior of the PUF 200. Differentinterleaver designs have been used in communication systems includingrandom interleaver, convolutional interleavers, random interleaver andS-random interleaver and may each be utilized in accordance with thepresent disclosure. In one specific embodiment, a random interleaver isutilized, in which the order for random shuffling is securely saved inPUF 200 to perform de-interleaving and generate a response.

The coding structure may be designed using code-offset techniques asdescribed below. In the challenge generation phase, PUF 200 readouts arequantized to 8 states and converted to a binary format using Grayencoding methods to generate a bit string w∈{0,1}^(n). Two codewords c₁and c₂ that are randomly selected from a linear block code set C_(n,k)with minimum distance d are added to w. The offset data between w and c₁and c₂ is called helper data (h₁=w+c₁, h₁=w+c₂)) and is publiclyavailable. In the response generation phase, a fuzzy version w′∈{0,1}^(n) is generated by the PUF 200 device, from which c₁′ and c₂′ arecalculated as c₁′=w′+h₁, c₂′=w′+h₂. The distance between c₁′ and c₂′with c is used to calculate the reliability information(soft-information). To further enhance security, the helper data can beencrypted using a Hash function or by the addition of redundantinformation.

In each decoding round, the extracted soft information can be used as aninput for a consecutive soft-decision module, hence the PUF key may bedetermined with a shortened string. The criteria to determine theoriginal codeword associated with current observation from the responseincludes selecting the codeword with minimum Euclidean distance. Thereliability of the decoded bits is given by the log likelihood ratio(LLR) of the decision.

A Chase-Pyndiah algorithm can be utilized for an iterative decoder tominimize the probability of error. In this approach, each decodercomponent receives soft input LLR information as a logarithm oflikelihood ratio (an estimate expressing the probability that thetransmitted data bit was equal to zero or one). Both decoder componentsprovide estimates of the same set of data bits in a different order.This information exchange process is continued in an iterative manneruntil converging with a desired accuracy. At each round, decodersre-evaluate their estimates, using information from the other decoder.The final output of the system can be extracted in soft format as thelikelihood of each binary bit or as the difference between the originalnoisy input and the final extracted info, as illustrated in FIG. 8B.

PUFs represent strong cryptographic primitives because a fresh responseis generated by the PUF hardware as often as needed to offer a secure,trusted authentication. Alterations to the PUF 200 due to foreignintervention, or attempts to present a fake challenge can be flagged bya negative authentication. The approaches described herein areconfigured to enhance the strength of PUFs by reducing the negativeinfluence of natural drifts and variations of the physical parametersunderlining the PUF 200. Other important factors in judging the strengthof PUFs are their unclonability, and their ability to block foreignentity access to secret information, such as the PUF challenge or themapping of the PUF's multiple states. PUFs are more or less unclonableas a function of their underlining parameters, and the integration ofthe PUF 200 within a secure element is an enhancing factor.

There are several approaches to improving security when multi-statearchitecture is involved. These include storing the mapping of themulti-state during challenge generation within an embedded secure memory(e.g., option A described above). With this option, the mapping is onlygenerated once, together with the challenges. However correctly securingthe secrecy of the storage is pivotal to the value of the method.

In some cases, a fresh mapping of the multi-states may be created duringresponse generation, and downloaded to the MLE 220 (e.g., option Bdescribed above). In this case no data is stored, and afterauthentication there is no information left to be stolen by third party.

Finally, in some implementations, the mapping of the PUF's multiplestates may be sent directly to the secure sever together with thechallenges. Assuming that all data transferred between the PUF 200 andthe secure server 230 is encrypted, this method may also be secure.

All three methods take advantage of the architecture presented in thisdisclosure.

In various embodiments, the present system and method provides for theuse of a multi-state memory 210 with n states to store the respectiveposition of PUF challenges of N bits sorted to reflect the profile ofthe physical parameters underlining the PUF 200. When the physicalparameter varies from a low value to a high value, several bits rankedat the bottom of the distribution are given state 0. The followingcollection of bits is given the state 1. This sorting process will endwith the last batch of these N bits, at the top of the distributionwhich are given the state n. The mapping of the respective position ofthe PUF response of N bits along the n states may reflect the physicalparameters underlining the PUF 200. This mapping may be performed duringthe PUF response generation cycle, and transferred to a securecomputational engine. The mapping of the respective position of the PUFresponses of N bits that are reflecting the physical parametersunderlining the PUF 200 may be performed during the PUF challengeprocess and communicated to an external secure processor.

The sorting of the N bits of the PUF challenge into n states may allowfor the usage of error detection computation methods between thechallenge, and the N bits of PUF responses that are tracking the profileof the physical parameters underlining the PUF 200. In someimplementations, the error detection can be exploited be a computationalengine to complete the authentication process that has the purpose tovalidate or invalidate that the challenge is satisfactory or not. Thecomputational engine may be a secure processor, a machine learningengine 220, a state machine, or any engine powerful enough to performthe secure authentication.

In some implementations, sensing elements are added to capture theparameters surrounding the PUF 200 and transfer them in thecomputational engine to improve the accuracy of the secureauthentication. These parameters include, but are not limited to,temperature, biasing conditions i.e. voltage and current,electro-magnetic interferences, acceleration, rotation, earth magneticfield, and mechanical stress.

In some implementations, authentication may be rendered more accuratethrough the use of a coding structure based on block turbo codes anditerative parallel decoding with soft decision making. The soft decodingmay provide information on the reliability of each bit. The codingstructure may utilize any of Max-Lloyd quantization to improve theaccuracy of the secure authentication, Gray coding to improve theaccuracy of the secure authentication, code-offset technique to improvethe coding structure, and Inter-leaver methods to shuffle the bits andimprove the coding structure. In some cases, hash functions, or paritybits are added to any of the data streams involved in the present systemand method. Data streams may include, but are not limited to,challenges, responses, vectors of data and errors, and learning databases.

In some implementations, machine learning techniques are used to predictand correct the portion of error in a CRP due to physical andenvironmental changes that were not captured by ECC. Independentcomponent analysis techniques may be used to break down remaining erroras a summation of multiple known error sources. The identified errorfrom any of the physical and environmental factors may be compared toavailable datasets to be predicted using a machine learning technique asdescribed herein. In some cases, the data steams are encrypted, orpartially encrypted, and then decrypted. Here, the term data streams mayrefer to, but is not limited to, challenges, responses, mapping ofmulti-states, vectors of data and errors, vectors of input, and learningdata bases.

This disclosure is intended to explain how to fashion and use variousembodiments in accordance with the invention rather than to limit thetrue, intended, and fair scope and spirit thereof. The foregoingdescription is not intended to be exhaustive or to limit the inventionto the precise form disclosed. Modifications or variations are possiblein light of the above teachings. The embodiment(s) was chosen anddescribed to provide the best illustration of the principles of theinvention and its practical application, and to enable one of ordinaryskill in the art to utilize the invention in various embodiments andwith various modifications as are suited to the particular usecontemplated. All such modifications and variations are within the scopeof the invention as determined by the appended claims, as may be amendedduring the pendency of this application for patent, and all equivalentsthereof, when interpreted in accordance with the breadth to which theyare fairly, legally, and equitably entitled.

What is claimed is:
 1. An authentication system for authenticating adevice, comprising: a physically unclonable function (PUF); a securememory; a sensing element configured to detect a physical parameter ofthe PUF; and a processor configured to: generate a challenge for achallenge response pair (CRP), wherein the CRP is used to authenticatethe device; retrieve, from the PUF, a response for the CRP based on thegenerated challenge, the response including a plurality of bits,associate each bit in the plurality of bits in the response with one ofthree or more groups, wherein bits associated with the same group aregenerated by cells in the PUF sharing a physical attribute; and store anindication of the association of each bit in the plurality of bits inthe response in the secure memory.
 2. The authentication system of claim1, wherein the processor is further configured to: use the indication ofthe association of each bit in the plurality of bits with the one of thethree or more groups to perform an authentication routine using thephysical parameter detected by the sensing element.
 3. Theauthentication system of claim 2, including a machine learning engineconfigured to use the indication of the association of each bit in theplurality of bits with the one of the three or more groups in the PUF,the physical parameter detected by the sensing element and a history ofprior responses from the PUF when analyzing a second response from thePUF.
 4. The authentication system of claim 2, wherein the sensingelement is configured to detect at least one of a temperature and a biascondition of the PUF.
 5. The authentication system of claim 2, whereinthe physical attribute comprises an input voltage for switching a cellstoring a logical value of “0” to a logical value of a “1” in the PUF.6. An authentication system for authenticating a device coupled to asecure server, comprising: a physically unclonable function (PUF); asecure memory; a sensing element configured to detect a physicalparameter of the PUF; and a processor configured to: receive, from thesecure server, a challenge for a challenge response pair (CRP), whereinthe CRP is used to authenticate the device; retrieve, from the PUF, aresponse for the CRP based on the received challenge, the responseincluding a plurality of bits, associate each bit in the plurality ofbits of the response with one of three or more groups, wherein bitsassociated with the same group are generated by cells in the PUF sharinga physical attribute, and store an indication of the association of eachbit in the plurality of bits in the response in the secure memory. 7.The authentication system of claim 6, wherein the processor is furtherconfigured to: use the indication of the association of each bit in theplurality of bits with the one of the three or more groups to perform anauthentication routine using the physical parameter detected by thesensing element.
 8. The authentication system of claim 7, including amachine learning engine configured to use the indication of theassociation of each bit in the plurality of bits with the one of thethree or more groups in the PUF, the physical parameter detected by thesensing element and a history of prior responses from the PUF whenanalyzing a second response from the PUF.
 9. The authentication systemof claim 7, wherein the sensing element is configured to detect at leastone of a temperature and a bias condition of the PUF.
 10. Theauthentication system of claim 7, wherein the physical attributecomprises an input voltage for switching a cell storing a logical valueof “0” to a logical value of a “1” in the PUF.
 11. The authenticationsystem of claim 6, wherein the processor is further configured to: upona determination that the challenge matches the response within apredetermined threshold value, generate a positive authentication. 12.An authentication system for authenticating a device coupled to a secureserver, comprising: a physically unclonable function; a secure memory; asensing element configured to detect a physical parameter of the PUF;and a processor configured to: receive, from the secure server, achallenge for a challenge response pair (CRP), wherein the CRP is usedto authenticate the device; retrieve, from the PUF, a response for theCRP based on the received challenge, the response including a pluralityof bits, associate each bit in the plurality of bits in the responsewith one of three or more groups, wherein bits associated with the samegroup are generated by cells in the PUF sharing a physical attribute,store an indication of the association of each bit in the plurality ofbits in the response in the secure memory, and authenticate the device.13. The authentication system of claim 12, wherein the processor isfurther configured to: use the indication of the association of each bitin the plurality of bits with the one of the three or more groups toperform an authentication routine using the physical parameter detectedby the sensing element.
 14. The authentication system of claim 13,including a machine learning engine configured to use the indication ofthe association of each bit in the plurality of bits with the one of thethree or more groups in the PUF, the physical parameter detected by thesensing element and a history of prior responses from the PUF whenanalyzing a second response from the PUF.
 15. The authentication systemof claim 13, wherein the sensing element is configured to detect atleast one of a temperature and a bias condition of the PUF.
 16. Theauthentication system of claim 13, wherein the physical attributecomprises an input voltage for switching a cell storing a logical valueof “0” to a logical value of a “1” in the PUF.
 17. The authenticationsystem of claim 12, wherein the processor is further configured to: upona determination that the challenge matches the response within apredetermined threshold value, generate a positive authentication.